So the area bounded by the curve is: A = 4a(sqrt(a2 + 4) + 1)/sqrt(a2 + 4)
To find the area bounded by the curve x=t−1/t and y=t+1/t, we can use integration. First, let's rearrange the equations to solve for t in terms of x and y:
x = t - 1/t
xt = t^2 - 1
t^2 - xt - 1 = 0
t = (x ± sqrt(x^2 + 4))/2
y = t + 1/t
yt = t^2 + 1
t^2 - yt + 1 = 0
t = (y ± sqrt(y^2 - 4))/2
Now, we need to determine the limits of integration. We can find these by setting the two expressions for t equal to each other:
(x + sqrt(x^2 + 4))/2 = (y + sqrt(y^2 - 4))/2
x + sqrt(x^2 + 4) = y + sqrt(y^2 - 4)
x - y = sqrt(y^2 - 4) - sqrt(x^2 + 4)
Squaring both sides, we get:
(x - y)^2 = (y^2 - 4) - 2sqrt(y^2 - 4)(x^2 + 4) + (x^2 + 4)
x^2 - 2xy + y^2 = x^2 + 4 - 2xy + y^2 - 2sqrt(y^2 - 4)(x^2 + 4)
-2sqrt(y^2 - 4)(x^2 + 4) = -4
sqrt(y^2 - 4)(x^2 + 4) = 2
y^2 - 4 = 2/(x^2 + 4)
y = ±sqrt(2/(x^2 + 4)) + 2
Since the curve is symmetric about the y-axis, we can just integrate from x = 0 to x = a, where a is the x-coordinate of the point where the curve intersects the y-axis. Setting x = 0 in the equation for y, we get:
y = ±sqrt(2)
So the area bounded by the curve is:
A = 2∫[0,a] y dx
A = 2∫[0,a] (sqrt(2/(x^2 + 4)) + 2) dx
This integral can be evaluated using a trigonometric substitution. Letting x = 2tanθ, we get:
dx = 2sec^2θ dθ
x^2 + 4 = 4tan^2θ + 4 = 4sec^2θ
sqrt(2/(x^2 + 4)) = sqrt(1/2sec^2θ) = cosθ/sqrt(2)
Substituting these expressions into the integral, we get:
A = 4∫[0,arctan(a/2)] cosθ dθ + 4a
Evaluating this integral, we get:
A = 4sin(arctan(a/2))/sqrt(2) + 4a
A = 4a/sqrt(a^2 + 4) + 4a
So the area bounded by the curve is: A = 4a(sqrt(a^2 + 4) + 1)/sqrt(a^2 + 4)
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. prove or disprove that if a, b, and d are integers with d > 0, then (a b) div d = a div d b div d
we can conclude that the statement "if a, b, and d are integers with d > 0, then (a b) div d = a div d b div d" is false.
We can prove that if a, b, and d are integers with d > 0, then (a + b) div d = a div d + b div d or disprove it by finding a counterexample.
Let's choose some specific values for a, b, and d to see if the equation holds. Let a = 8, b = 5, and d = 3.
(a + b) div d = (8 + 5) div 3 = 13 div 3 = 4
a div d + b div d = 8 div 3 + 5 div 3 = 2 + 1 = 3
Since (a + b) div d ≠ a div d + b div d for our chosen values of a, b, and d, we have found a counterexample that disproves the equation.
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Use implicit differentiation to find
∂z/∂x and ∂z/∂y.
x2 + 4y2 + 9z2 = 4
The partial derivatives using implicit differentiation are:
∂z/∂x = -x / (9z)
∂z/∂y = -4y / (9z)
To find the partial derivatives ∂z/∂x and ∂z/∂y using implicit differentiation, we start with the given equation:
x^2 + 4y^2 + 9z^2 = 4
First, we differentiate both sides of the equation with respect to x:
2x + 0 + 18z(∂z/∂x) = 0
Now, solve for ∂z/∂x:
18z(∂z/∂x) = -2x
∂z/∂x = -2x / (18z)
∂z/∂x = -x / (9z)
Next, we differentiate both sides of the equation with respect to y:
0 + 8y + 18z(∂z/∂y) = 0
Now, solve for ∂z/∂y:
18z(∂z/∂y) = -8y
∂z/∂y = -8y / (18z)
∂z/∂y = -4y / (9z)
So, the partial derivatives are:
∂z/∂x = -x / (9z)
∂z/∂y = -4y / (9z)
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Write Yes if the situation is an example of random sampling. Write No if the situation is not. State your reason for your answer.
1. The teacher asked the first 5 students on her class seating chart to write down where the class should go on a field trip.
2. Clara surveyed more than half the teachers at her school and then, without looking, selected the responses for her sample.
3. To get a random sampling of every student in her school, Cheryl surveyed all the students in her math class.
4. A company sent e-mails to its customers asking them to e-mail back their opinion of the company’s products. Only 10 of them e-mailed back.
The teacher asked the first 5 students on her class seating chart to write down where the class should go on a field trip is yes
Clara surveyed more than half the teachers at her school and then, without looking, selected the responses for her sample is no
To get a random sampling of every student in her school, Cheryl surveyed all the students in her math class is no
A company sent e-mails to its customers asking them to e-mail back their opinion of the company’s products. Only 10 of them e-mailed back is no
1) Yes, this is an example of random sampling.
The teacher used a systematic method of selecting the first 5 students on her seating chart to ensure that the sample is representative of the class.
2) No, this is not an example of random sampling.
Clara did not use a random selection method to choose the responses for her sample, which can result in a biased sample.
3) No, this is not an example of random sampling.
Cheryl only surveyed the students in her math class, which is not a representative sample of the entire school population.
4) No, this is not an example of random sampling.
The sample is not representative of the entire customer population since only 10 customers responded.
This may lead to biased results if the 10 customers who responded have different opinions than those who did not respond.
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1. Find the area of the composite figure.
6 ft
5 ft
3 ft-
3ft
T
2 ft
1
Answer: 48
Step-by-step explanation: we can split this into a trapezoid and a rectangle. The area of the rectangle is 6*5 = 30.
प
3
16. The function h = -161² + 32 +9 represents the height h (in feet) of a ball t seconds after it is thrown into the air.
a. Find the maximum height of the ball.
b. Graph the function.
The maximum height of the ball is 9.29 feet.
The given function is h(t) = -161t²+32t+9
To find the maximum height of the ball, we need to find the vertex of the quadratic function.
The vertex of the parabola with equation h = ax² + bx + c is given by the point (-b/2a, f(-b/2a)).
In this case, a = -161, b = 32, and c = 9
so the vertex is located at t = -b/2a
= -32/2(-161)
= 0.1 seconds.
Plugging this value into the equation, we get the height
h = -161(0.1)² + 32(0.1) + 9
= 9.29 feet
Therefore, the maximum height of the ball is 9.29 feet.
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someone help me on this pleasee
The complete table.
x -8 -4 0 4 8
y 28 16 4 -8 -20
We have,
y = -3x + 4
Now,
Substituting x = -8, -4, 0, 4, and 8.
y = -3 x -8 + 4 = 24 + 4 = 28
y = -3 x -4 + 4 = 12 + 4 = 16
y = -3 x 0 + 4 = 0 + 4 = 4
y = -3 x 4 + 4 = -12 + 4 = -8
y = -3 x 8 + 4 = -24 + 4 = -20
Thus,
The complete table.
x -8 -4 0 4 8
y 28 16 4 -8 -20
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(a) If sup A < sup B, show that there exists an element b ∈ B that is an upper bound for A.
(b) Give an example to show that this is not always the case if we only assume sup A ≤ sup B.
(a) We have shown that there exists an element b ∈ B that is an upper bound for A.
(b) The statement in part (a) is not always the case if we only assume sup A ≤ sup B.
(a) If sup A < sup B, show that there exists an element b ∈ B that is an upper bound for A.
Proof:
1. By definition, sup A is the least upper bound for set A, and sup B is the least upper bound for set B.
2. Since sup A < sup B, there must be a value between sup A and sup B.
3. Let's call this value x, where sup A < x < sup B.
4. Now, since x < sup B and sup B is the least upper bound of set B, there must be an element b ∈ B such that b > x (otherwise, x would be the least upper bound for B, which contradicts the definition of sup B).
5. Since x > sup A and b > x, it follows that b > sup A.
6. As sup A is an upper bound for A, it implies that b is also an upper bound for A (b > sup A ≥ every element in A).
Thus, we have shown that there exists an element b ∈ B that is an upper bound for A.
(b) Give an example to show that this is not always the case if we only assume sup A ≤ sup B.
Example:
Let A = {1, 2, 3} and B = {3, 4, 5}.
Here, sup A = 3 and sup B = 5. We can see that sup A ≤ sup B, but there is no element b ∈ B that is an upper bound for A, as the smallest element in B (3) is equal to the largest element in A, but not greater than it.
This example shows that the statement in part (a) is not always the case if we only assume sup A ≤ sup B.
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Most large companies rely on one person to evaluate systems requests instead of relying on a systems review committee.
true or false
Most large companies rely on one person to evaluate system time requests instead of relying on a systems review committee. The above statement is true.
Most large companies do not rely on just one person to evaluate system requests. They typically rely on a systems review committee, which consists of multiple individuals with diverse expertise, to make more informed and balanced decisions regarding their systems.
Many small companies rely on a single person rather than a group of people to evaluate demand. The request is reasonable if possible. Attaching a report required by new federal law is an example of a blank check project. Limitations may include hardware, software, time, authorization, rights or cost.
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Brandon bought 3 hot dogs and 2 sodas for $14.50 Carson bought 4 hot dogs and 1 soda for $16 how much did each cost?
When computing the degrees of freedom for ANOVA, how is the between-group estimate calculated?a. (n - 1)/kb. n - 1c. k - 1d. N - k
The correct option for calculating the degrees of freedom for the between-group estimate in ANOVA is: c. k - 1
Here's a step-by-step explanation:
1. ANOVA, or Analysis of Variance, is a statistical method used to compare the means of multiple groups to determine if there are significant differences between them. In this context, "k" represents the number of groups being compared, and "N" represents the total number of observations.
2. Degrees of freedom (df) are used in statistical tests to account for variability in the data. They are essentially the number of values that can vary independently in the calculation of a statistic.
3. In ANOVA, there are two types of degrees of freedom: between-group (df_between) and within-group (df_within).
4. To calculate the between-group degrees of freedom (df_between), we use the formula: df_between = k - 1. This is because there are k groups being compared, and each group contributes one degree of freedom, minus one since we are comparing the groups against each other.
5. The within-group degrees of freedom (df_within) would be calculated using the formula: df_within = N - k, which accounts for the total number of observations minus the number of groups.
In summary, to compute the degrees of freedom for the between-group estimate in ANOVA, you would use the formula df_between = k - 1.
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the lower class limit represents the smallest data value that can be included in the class.True/False
the lower class limit represents the smallest data value that can be included in the classThe statement is true.
The lower class limit is the smallest value that can be included in a class interval.
Therefore, the statement is correct.
The lower class limit represents the smallest data value that can be included in a particular class. In a frequency distribution table, data values are grouped into classes, and each class has a lower and upper class limit. The lower class limit denotes the lowest value within that class, and any data value equal to or greater than the lower limit but less than the upper limit falls into that class.
The statement is true, as the lower-class limit indeed represents the smallest data value that can be included in the class.
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Redo Exercise 9 of Section 7.6 using Stokes' theorem. 9. Evaluate S/s (V x F)ds, where S is the surface x2 + y2 + 3z2 = 1,2 < 0 and F is the vector field F = yi - xj + zxy?k. (Let n, the unit normal, be upward pointing.)
Answer: The value of the surface integral is 2π/3.
Step-by-step explanation:
To apply Stokes' theorem, we need to find the curl of the vector field F:
curl F = (dF_z/dy - dF_y/dz)i + (dF_x/dz - dF_z/dx)j + (dF_y/dx - dF_x/dy)k
= xyi + k
Now, we can apply Stokes' theorem:
∫∫S curl F · dS = ∫C F · dr
where S is the surface bounded by the curve C, and dS is the outward-pointing normal vector to S.
First, we need to parameterize the surface S. We can use cylindrical coordinates, since the surface has rotational symmetry around the z-axis:
x = r cosθ
y = r sinθ
z = √(1 - r^2 - 3z^2)
where 0 ≤ r ≤ 1/√(3), and 0 ≤ θ ≤ 2π.
The normal vector to S is
dS = (∂z/∂r × ∂z/∂θ, ∂x/∂r × ∂x/∂θ, ∂y/∂r × ∂y/∂θ)
= (3r^2 cosθ, -3r^2 sinθ, 1 - 2r^2)
Since n is upward-pointing, we need to flip the sign of the z-component of dS. Thus, we have:
dS = (-3r^2 cosθ, 3r^2 sinθ, 2r^2 - 1)
Next, we need to find the curve C, which is the boundary of S. Since S lies on the plane z = -2, we have:
x^2 + y^2 + 3z^2 = 1
r^2 + 3z^2 = 1
z = -2, or r = 1/√(3)
Thus, the curve C consists of two circles of radius 1/√(3) in the planes z = ±√(2/3). We can parameterize these circles as:
r = 1/√(3)
θ = t
z = √(2/3)
and
r = 1/√(3)
θ = t
z = -√(2/3)
where 0 ≤ t ≤ 2π.
Now, we can evaluate the line integral:
∫C F · dr = ∫C (yi - xj + zxy·k) · dr
= ∫C (r sinθ i - r cosθ j + √(1 - r^2 - 3z^2) r^2 sinθ cosθ k) · (dr/dt) dt
= ∫0^2π (-(1/√3) sin t i - (1/√3) cos t j - (2/3) (cos^2 t - sin^2 t) k) · (-1/√3 sin t i + 1/√3 cos t j) dt
= ∫0^2π (1/3 sin^2 t + 1/3 cos^2 t) dt
= 2π/3
Finally, we can use Stokes' theorem to find the surface integral:
∫∫S curl F · dS = ∫C F · dr = 2π/3
Therefore, the value of the surface integral is 2π/3.
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Arthur played a basketball game at a carnival. He made 47 baskets before time ran out. He earned 13 tickets for each basket he made. Then, he went to the prize counter. Each prize cost 9 tickets. How many prizes can Arthur get?
Answer: 67
explanation:
47 x 13 = 611 -- so this is how many tickets he has total
611 / 9 = 67.9
So he can get 67 prizes.
a way you can check if this is right is by multiplying 67 by 9 and you see that is 603, and he has 611 tickets so he will even have a few tickets left over. but he can not get 68 prizes because if you see what 68 x 9 is, it is 612 which is one ticket more than what he has so he cant get it. So the max he can get is 67
Answer:
67
Step-by-step explanation:
We know that, in total, he made 47 baskets, and each basket is 13 tickets.
So in total, he made 611 tickets:
47·13
=611
Next, he wanted to get [a] prize(s), but each prize costs 9 tickets, we divide the total number of tickets he has by the prize cost.
611/9
=67.88...
You obviously can't get 0.88 of a prize, so the max amount of prizes that Arthur can get is 67.
Hope this helps! :)
If y = 4 find slope, X-intercept and y-intercept.
Answer:
An equation in the form y = mx + b is in the 'slope y-intercept' form where m is the slope and b is the y-intercept. We can rewrite our equation, y = 4, in slope y-intercept form as follows: y = 0x + 4. Here, it is clear that the slope, or m, is zero. Therefore, the slope of the horizontal line y = 4 is zero
determine the z-coordinate of the mass center of the homogeneous paraboloid of revolution shown.
The z-coordinate of the mass center of the homogeneous paraboloid of revolution shown is (12/5) units.
The determination of the z-coordinate of the mass center of the homogeneous paraboloid of revolution requires a long answer.
Firstly, we need to define the mass density of the paraboloid. Since it is a homogeneous object, its mass density is constant throughout its volume.
Let us denote this density as ρ.
Next, we need to find the volume of the paraboloid.
The volume of a paraboloid of revolution with a height h and a base radius r is given by V = (π/2) * r^2 * h/3.
In this case, the height of the paraboloid is 4 units and the radius of the base is 2 units. Thus, the volume of the paraboloid is:
V = (π/2) * (2)^2 * 4/3 = (8π/3) units^3
Now, we can find the mass of the paraboloid by multiplying its volume by its density:
M = ρ * V = ρ * (8π/3) units^3
The next step is to find the x and y coordinates of the mass center of the paraboloid.
We can do this by using double integrals:
x = (1/M) * ∬(paraboloid) x * ρ * dV
y = (1/M) * ∬(paraboloid) y * ρ * dV
Since the paraboloid is symmetric about the z-axis, we know that its mass center will lie on this axis, and thus, its x and y coordinates will be zero.
Finally, we need to find the z-coordinate of the mass center. We can do this by using the same double integral, but this time we integrate over the z-axis:
z = (1/M) * ∬(paraboloid) z * ρ * dV
To set up the double integral, we can use cylindrical coordinates, with ρ ranging from 0 to 2 and θ ranging from 0 to 2π.
The z-coordinate of any point on the paraboloid is given by z = (1/16) * (x^2 + y^2), so we can substitute this into the double integral:
z = (1/M) * ∫(0 to 2π) ∫(0 to 2) ∫(0 to (1/16)*(ρ^2)) ρ * z * ρ * ρ * dρ dθ dz
After evaluating this integral, we get:
z = (3/5) * h = (12/5) units
Therefore, the z-coordinate of the mass center of the homogeneous paraboloid of revolution shown is (12/5) units.
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consider a device with 7 parts. for the device to work properly, at least one of the parts need to work. if each part works with probability p=0.216, what is the probability that the device will work?
Therefore, The probability that the device will work is 0.634 or 63.4%.
This problem can be solved using the complement rule. The complement of the device working is all the parts failing. Therefore, the probability of the device not working is (1 - 0.216)^7 = 0.366. To find the probability of the device working, we subtract this from 1:
1 - 0.366 = 0.634.
To find the probability that the device will work, we'll use the complementary probability. This means we'll first find the probability that all parts fail and then subtract it from 1. Let's denote the probability of a part failing as q, which is equal to 1 - p.
Step 1: Calculate q.
q = 1 - p = 1 - 0.216 = 0.784
Step 2: Calculate the probability of all parts failing.
P(all parts fail) = q^7 = 0.784^7 ≈ 0.1278
Step 3: Calculate the probability that the device will work.
P(device works) = 1 - P(all parts fail) = 1 - 0.1278 ≈ 0.8722
In conclusion, the probability that the device will work is approximately 0.8722.
Therefore, The probability that the device will work is 0.634 or 63.4%.
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On a test that has a normal distribution, a score of 53 falls two standard deviations above the mean, and a score of 33 falls two standard deviations below the mean. Determine the mean of this test.
The solution is: A score of approximately 38.2 separates the top 53% from the bottom 47% on this English test.
Here, we have,
We can use the inverse normal distribution function to find the z-score corresponding to the desired percentile, and then use the formula for standardizing a normal variable to find the corresponding raw score.
The score that separates the top 53% from the bottom 47% on an English test with a normal distribution, mean of 37.6, and standard deviation of 7.6 can be found using the inverse normal distribution function.
We need to find the z-score that corresponds to the 53rd percentile. We can do this using a standard normal distribution table or a calculator. The z-score corresponding to the 53rd percentile is approximately 0.07.
We can use the formula for standardizing a normal variable to find the corresponding raw score: z = (X - mean) / standard deviation Rearranging this formula, we get: X = z * standard deviation + mean
Plugging in the values we have: X = 0.07 * 7.6 + 37.6 X ≈ 38.2
A score of approximately 38.2 separates the top 53% from the bottom 47% on this English test.
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complete question:
scores on an english test are normally distributed with a mean of 37.6 and a standard deviation of 7.6. find the score that separates the top 53% from the bottom 47%
Someone please I’m desperate (helppp answer this math problem)
Anyone who knows how to do this correctly write an expression for the perimeter shape. thanks
Answer:
8x + 8y + 16
Step-by-step explanation:
It is simple perimeter is the sum of all side of the polygon (figure) so
P = (4X+5) + (2Y) + (X+5) + (2Y+3) + (3X) + (4Y+3)
I write
(4X+5) b/c it is one side of the figure (2Y) b/c it is one side of the figure too (X+5) by subtracting (3X) from (4X+5) (2Y+3) b/c it is one side of the figure(3X) b/c it is one side of the figure(4Y+3) by taking the sum of the 2 opposite side (2Y) and (2Y+3).so
P = (4X+5) + (2Y) + (X+5) + (2Y+3) + (3X) + (4Y+3)
P = 8x + 8y + 16
so the perimeter of the figere is 8x + 8y + 16
A photo of a beetle in a science book is increased to 555% as large as the actual size. If the beetle is 14 millimeters, what is the size of the beetle in the photo?
A photo of a beetle in a science book is increased to 555% as large as the actual size. If the beetle is 14 millimeters. The size of the beetle in the photo is 77.7 millimeters.
To determine the size of the beetle in the photo, we can multiply its actual size by the percentage increase in size. 555% can also be expressed as a decimal, 5.55. Therefore, to find the size of the beetle in the photo, we multiply 14 millimeters by 5.55, which gives us 77.7 millimeters. This means that the beetle appears to be almost six times larger in the photo than its actual size. It's important to note that the size of the beetle in the photo may vary depending on the size of the book it's printed in or the resolution of the image.
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use technology or a z-distribution table to find the indicated area. suppose ages of cars driven by company employees are normally distributed with a mean of 8 years and a standard deviation of 3.2 years. approximately 75% of cars driven by company employees are older than what age?
Over 10.144 years of age are found in 75% of firm employees' autos.
We need to identify the z-score that corresponds to the age of the cars driven by firm employees that are 75% older than the other cars of 75th percentile of the normal distribution.
A normal distribution calculator or statistical software programme can be used to find this z-score. As an alternative, we can look for the value using a z-distribution table.
The formula for the z-score is:
z = (x - μ) / σ
If x is the value we are looking for, is the distribution's mean, and is its standard deviation.
We can use the common normal distribution table or a calculator with a built-in function to determine the z-score corresponding to the 75th percentile to a cumulative probability of 0.75. The table value is 0.67.
As a result, we can determine the age of the company vehicles that are approximately 75% older than the others as follows:
x = μ + zσ
= 8 + (0.67)(3.2)
= 10.144
As a result, more than 75% of the cars that firm employees drive are older than 10.144 years.
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Use the given minimum and maximum data entries, and the number of classes, to find the class width, the lower class limits, and the upper class limits. minimum = 8, maximum=79, 7 classes
The upper class limits are- 29, 39, 49, 59, 69, 79, 89
The lower class limits are- 20, 30, 40, 50, 60, 70, 80
The class midpoints are- 24.5, 24.5, 44.5, 54.5, 64.5, 74.5, 84.5
The class boundaries are- 29.5, 39.5, 49.5, 59.5, 69.5, 79.5
And the number of individuals included in the summary is 84.
Here, we are given the following dataset-
Age (yr) when Frequency
award was won
20-29 27
30-39 32
40-49 15
50-59 3
60-69 5
70-79 1
80-89 1
Upper class limit is the largest data value that can go in a class.
Thus, the upper class limits are- 29, 39, 49, 59, 69, 79, 89
Lower class limit is the smallest data value that can go in a class.
Thus, the lower class limits are- 20, 30, 40, 50, 60, 70, 80
The class midpoint is the average of the upper and lower limits of a class. Class midpoint = (upper limit + lower limit)/ 2
Thus, the class midpoints are- 24.5, 24.5, 44.5, 54.5, 64.5, 74.5, 84.5
Class boundary is the midpoint of the upper class limit of a class and the lower class limit of the previous class.
Thus, the class boundaries are- 29.5, 39.5, 49.5, 59.5, 69.5, 79.5
Frequency gives us the number of individuals/ objects belonging to a particular class.
Thus, the number of individuals included in the summary = 27 + 32 + 15 + 3 + 5 + 1 + 1 = 84
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complete question:
Identify the lower class limits, upper class limits,
class width, class midpoints, and class boundaries for
the given frequency distribution. Also identify the
number of individuals included in the summary.
Age (yr) when
award was won
20-29
30-39
40-49
50-59
60-69
70-79
80-89
Frequency
27
32
15
3
5
1
1
In an analysis of variance, you reject the null hypothesis when the F ratio is a. negative b. much larger than 1. c. equal to the t score. d. smaller than 1.
In an analysis of variance, you reject the null hypothesis when the F ratio is:
b. much larger than 1.
Here's a step-by-step explanation:
1. The null hypothesis states that there are no significant differences among the groups being compared.
2. Variance is the measure of how much the individual data points in a dataset vary from the mean.
3. The F ratio is the ratio of two variances, specifically, the variance between group means and the variance within groups.
4. When the F ratio is much larger than 1, it indicates that the variance between group means is much larger than the variance within groups.
5. This suggests that there is a significant difference among the group means, leading to the rejection of the null hypothesis.
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1. Given: f(x) = (x + 7) (2x − 3) and g(x) = (x + 7).
Find g(z)) f(z).
2. Given: f(x) = (5x+7) (-3x+11) and g(x) = (-3x + 11).
Find g (z))f(z).
1) The value of function is,
⇒ (2x − 3)
2) The value of function is,
⇒ (5x + 7)
We have to given that;
Functions are,
f(x) = (x + 7) (2x − 3) and g(x) = (x + 7).
Hence, We get;
⇒ f (x) / g (x)
⇒ (x + 7) (2x − 3) / (x + 7)
⇒ (2x − 3)
And, Functions are,
f(x) = (5x+7) (-3x+11) and g(x) = (-3x + 11).
Hence, We get;
⇒ f (x) / g (x)
⇒ (5x+7) (-3x+11) / (-3x + 11).
⇒ (5x + 7)
Thus, 1) The value of function is,
⇒ (2x − 3)
2) The value of function is,
⇒ (5x + 7)
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Let X1,…,Xn be an independent trials process, and S∗n be their standardized sum. What is limn→[infinity]P(−0.28
If X1,…,Xn be an independent trials process, and S∗n be their standardized sum then,
limn→[infinity]P(S∗n > -0.28) = 0.6103
To answer this question, we need to use the central limit theorem. The central limit theorem states that if we have a large enough sample size, the distribution of the standardized sum (S∗n) approaches a normal distribution.
In this case, we want to find the limit of the probability that S∗n is greater than -0.28 as n approaches infinity.
Let Z be a standard normal random variable, then:
P(S∗n > -0.28) = P((S∗n - E[S∗n]) / sqrt(Var[S∗n]) > (-0.28 - E[S∗n]) / sqrt(Var[S∗n]))
= P(Z > (-0.28 - 0) / 1)
= P(Z > -0.28)
Using a standard normal distribution table, we can find that P(Z > -0.28) is approximately 0.6103.
Therefore, limn→[infinity]P(S∗n > -0.28) = 0.6103, since as n approaches infinity, S∗n approaches a standard normal distribution.
The correct question should be :
Let X1,…,Xn be an independent trials process, and S∗n be their standardized sum. What is limn→[infinity]P(S∗n > -0.28)?
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a) what’s the size of angel a?
b) Use your answer from part a) to work out the size of reflex angle b
Give your answers to the nearest degree
The value of the size of angel a is, 100 degree
And, The value of size of angle b is, 280 degree
We have to given that;
Figure is shown in figure.
Now, By measuring of angle we get;
The value of the size of angel a is,
⇒ ∠ a = 100 - 0 degree
⇒ ∠ a = 100 degree
And, The value of size of angle b is,
⇒ ∠ b = 180° + 100°
⇒ ∠b = 280°
Thus, The value of the size of angel a is, 100 degree
And, The value of size of angle b is, 280 degree
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A 20 foot pole has a cable that enters the ground 3 feet away from the base of the pole. How much cable is needed to connect to the ground? Round to the nearest tenth.
Approximately 19.8 feet of cable is needed to connect the pole to the ground.
To calculate the length of the cable needed to connect the 20-foot pole to the ground, we can use the Pythagorean theorem.
The Pythagorean theorem states that in a right triangle, the square of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the other two sides.
In this case, the pole acts as the hypotenuse, the distance from the base of the pole to the ground acts as one side, and the length of the cable acts as the other side.
Using the Pythagorean theorem, we can find the length of the cable:
Length of cable = √(Length of pole^2 - Distance^2)
= √(20^2 - 3^2)
= √(400 - 9)
= √391
≈ 19.8 feet (rounded to the nearest tenth)
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Can someone help me with this middle school math problem it’s unknown number’s. 192-__=-1
Answer:
is it 193
Step-by-step explanation:
i added -1 and 192
Indicate below weather the equation in the box is true or false
Answer:
False
Step-by-step explanation:
4/8 equals to 1/2 but 6/10 equals to 3/5. Correct would be if it was 5/10
A stainless steel patio heater is in a square pyramid. The length of one side of the base is 22. 6 in. The slant height of the pyramid is 87. 9 in. What is the height of the pyramid?
PLS HELP FAST!!
The height of the pyramid is approximately 86.4 inches.
The square pyramid can be divided into four identical triangles. Each triangle has a base equal to one side of the square base and a height equal to the height of the pyramid. The slant height of the pyramid is the hypotenuse of each of these triangles.
Using the Pythagorean theorem, we can find the height of each triangle (and hence the height of the pyramid):
h^2 + (22.6/2)^2 = 87.9^2
Simplifying the equation:
h^2 + 255.76 = 7728.41
h^2 = 7472.65
h ≈ 86.4
Therefore, the height of the pyramid is approximately 86.4 inches.
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a rectangular restaurant kitchen has an area of 91 square meters. its perimeter is 40 meters. what are the dimensions of the kitchen?
Let's assume that the length of the rectangular kitchen is L and the width is W. We know that the area of the kitchen is 91 square meters, so we can write:
L x W = 91
We also know that the perimeter of the kitchen is 40 meters, which means:
2L + 2W = 40
We can simplify this equation by dividing both sides by 2:
L + W = 20
Now we have two equations:
L x W = 91
L + W = 20
We can use substitution to solve for one of the variables. Let's solve for L:
L = 20 - W
Now we can substitute this expression for L in the first equation:
(20 - W) x W = 91
Expanding this equation gives us a quadratic equation:
W^2 - 20W + 91 = 0
We can solve for W using the quadratic formula:
W = (20 ± √(20^2 - 4 x 1 x 91)) / (2 x 1)
W = (20 ± 3) / 2
W = 11 or W = 9
If W is 11, then L is 9. If W is 9, then L is 11. Therefore, the dimensions of the kitchen are either 9 meters by 11 meters or 11 meters by 9 meters.
In summary, we can use the area and perimeter of a rectangular shape to find its dimensions by setting up equations and solving for the variables. In this case, we used substitution and the quadratic formula to find the possible dimensions of a rectangular kitchen with an area of 91 square meters and a perimeter of 40 metres.
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